Suppose that a red die and a green die are tossed and the numbers on the sides that face upward are observed. (a) what is the probability that the sum of the numbers is less than 4

First of all, let's count how many events compose our sample space: since we are rolling two dice, and each of them has six sides, the sample space has 36 possible events, given by all couples , with

Then, we observe that none of the die can give 4 or more, otherwise the sum of the two dice would be at least 5.

So, we have the following possible outcomes:

Red die gives 1, green die gives 3

Both dice give 2

Red die gives 3, green die gives 1.

These are three events out of the 36 possible events, so their probability is

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